Step 1: Beyond the generic cephalosporin reactions, examiners test the drug-specific toxicities. So the task is to match thrombocytopenia to the one agent that owns it.
Step 2: The marrow-related effects of neutropenia together with thrombocytopenia are the recognised fingerprint of ceftazidime. Therefore ceftazidime is the answer.
Step 3: Separating the others: cefoperazone is the bleeding-and-disulfiram drug (its side chain interferes with vitamin K dependent clotting factors and with alcohol metabolism), while cefixime and cefdinir are oral agents whose dominant complaint is diarrhea. None of these three is the textbook cause of a low platelet count.
\[\boxed{\text{Ceftazidime}}\]